In this study, the deposition of fibrous particles in a realistic 3D model of the right nasal cavity of a 24-years-old woman was simulated using the non-creeping formulations for hydrodynamic forces and torques. The Lagrangian trajectory analysis approach within the Ansys-Fluent software was used for these simulations. Several user-defined functions (UDFs) for solving the coupled translational and rotational motion of an ellipsoidal fiber and for evaluation of non-creeping forces and torques were developed and were incorporated in the Ansys-Fluent DPM. The passage included the main nasal cavity from the nostril to the beginning of the nasopharynx. Both laminar and turbulent steady inhalation breathing conditions were assumed, and for turbulence modeling, the Realizable k-ε model was employed. It was assumed that the airflow was incompressible. The breathing rates of 2.5, 5.0, 7.5, and 10 lit/min per nostril were considered for laminar airflow corresponding to the rest or light physical activity conditions. For turbulent airflow, the breathing rates of 15, 20, and 30 lit/min were assumed for high physical activities. The transport and deposition of fibers of different sizes and aspect ratios in the nasal cavity under laminar and turbulent airflow regimes were investigated.The simulation results showed that the increase of air flow rate, fiber diameter, and aspect ratio led to the increase of deposition in the human nasal cavity. In addition, the use of forces and torques estimated from the more accurate non-creeping flow estimation led to somewhat lower particle deposition in the nasal cavity compared to those obtained from the simplified creeping flow assumption.